Heat exchangers (LMTD) worksheet with answers

Free printable Heat exchangers (LMTD) worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
lengthT90 °C75 °C15 °C60 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 90 to 75 °C while the cold fluid heats from 15 to 60 °C. Find the log-mean temperature difference ΔTlm.

Th: 90 → 75 °CTc: 15 → 60 °C
ΔTlm = K
2.Easy
lengthT140 °C105 °C40 °C30 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 140 to 105 °C while the cold fluid heats from 30 to 40 °C. Find the log-mean temperature difference ΔTlm.

Th: 140 → 105 °CTc: 30 → 40 °C
ΔTlm = K
3.Medium
lengthT180 °C105 °C15 °C30 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 440 kW. The hot fluid cools from 180 to 105 °C and the cold fluid heats from 15 to 30 °C. The overall heat transfer coefficient is 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 440 kWU = 500 W/(m²·K)Th: 180 → 105 °CTc: 15 → 30 °C
A = m²
4.Medium
lengthT85 °C50 °C10 °C30 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 300 kW. The hot fluid cools from 85 to 50 °C and the cold fluid heats from 10 to 30 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 300 kWU = 1000 W/(m²·K)Th: 85 → 50 °CTc: 10 → 30 °C
A = m²
5.Hard
lengthT100 °C75 °C69.81 °C10 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.5 kJ/(kg·K)) cools from 100 to 75 °C in a counter-flow exchanger. It heats 0.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 10 °C. With U = 300 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.5 kJ/(kg·K)Th: 100 → 75 °Cṁc = 0.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °CU = 300 W/(m²·K)
A = m²
6.Hard
lengthT90 °C60 °C34.13 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.3 kJ/(kg·K)) cools from 90 to 60 °C in a counter-flow exchanger. It heats 2 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 30 °C. With U = 500 W/(m²·K), find the heat transfer area A needed.

ṁh = 0.5 kg/scp,h = 2.3 kJ/(kg·K)Th: 90 → 60 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 500 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 37.28 K
  2. 2. ΔTlm = 86.9 K
  3. 3. A = 7.709 m²
  4. 4. A = 7.21 m²
  5. 5. A = 9.179 m²
  6. 6. A = 1.658 m²

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